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Mirrors > Home > ILE Home > Th. List > ralrnmpo | Unicode version |
Description: A restricted quantifier over an image set. (Contributed by Mario Carneiro, 1-Sep-2015.) |
Ref | Expression |
---|---|
rngop.1 | |
ralrnmpo.2 |
Ref | Expression |
---|---|
ralrnmpo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rngop.1 | . . . . 5 | |
2 | 1 | rnmpo 5881 | . . . 4 |
3 | 2 | raleqi 2630 | . . 3 |
4 | eqeq1 2146 | . . . . 5 | |
5 | 4 | 2rexbidv 2460 | . . . 4 |
6 | 5 | ralab 2844 | . . 3 |
7 | ralcom4 2708 | . . . 4 | |
8 | r19.23v 2541 | . . . . 5 | |
9 | 8 | albii 1446 | . . . 4 |
10 | 7, 9 | bitr2i 184 | . . 3 |
11 | 3, 6, 10 | 3bitri 205 | . 2 |
12 | ralcom4 2708 | . . . . . 6 | |
13 | r19.23v 2541 | . . . . . . 7 | |
14 | 13 | albii 1446 | . . . . . 6 |
15 | 12, 14 | bitri 183 | . . . . 5 |
16 | nfv 1508 | . . . . . . . 8 | |
17 | ralrnmpo.2 | . . . . . . . 8 | |
18 | 16, 17 | ceqsalg 2714 | . . . . . . 7 |
19 | 18 | ralimi 2495 | . . . . . 6 |
20 | ralbi 2564 | . . . . . 6 | |
21 | 19, 20 | syl 14 | . . . . 5 |
22 | 15, 21 | syl5bbr 193 | . . . 4 |
23 | 22 | ralimi 2495 | . . 3 |
24 | ralbi 2564 | . . 3 | |
25 | 23, 24 | syl 14 | . 2 |
26 | 11, 25 | syl5bb 191 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wceq 1331 wcel 1480 cab 2125 wral 2416 wrex 2417 crn 4540 cmpo 5776 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-cnv 4547 df-dm 4549 df-rn 4550 df-oprab 5778 df-mpo 5779 |
This theorem is referenced by: txcnp 12440 txcnmpt 12442 |
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